1. The polynomial in form a^3 + b^3 is called the sum of two cubes because two cubic terms are being added together. The binomial factor on the right side of the equation has a middle sign that is positive. The middle sign of the trinomial factor will always be opposite, negative.
Formula:
a^3 + b^3 = ( a + b ) ( a^2 - ab + b^2 )
The polynomial in the form of a^3 - b^3 is called the difference of two cubes because two cubic terms are being subtracted. The binomial factor on the right side of the equation has a middle sign that is negative. The middle sign of the trinomial factor will always be opposite, positive.
Formula:
a^3 - b^3 = ( a - b ) ( a^2 + ab + b^2 )
2. Simply factor out 3 from the existing exponents of x and y.
Use the law of exponent known as the power to power rule to justify this step.
( We take out 3 because to be a cube implies that any expression must have an outer exponent,
Answers & Comments
1. The polynomial in form a^3 + b^3 is called the sum of two cubes because two cubic terms are being added together. The binomial factor on the right side of the equation has a middle sign that is positive. The middle sign of the trinomial factor will always be opposite, negative.
Formula:
a^3 + b^3 = ( a + b ) ( a^2 - ab + b^2 )
The polynomial in the form of a^3 - b^3 is called the difference of two cubes because two cubic terms are being subtracted. The binomial factor on the right side of the equation has a middle sign that is negative. The middle sign of the trinomial factor will always be opposite, positive.
Formula:
a^3 - b^3 = ( a - b ) ( a^2 + ab + b^2 )
2. Simply factor out 3 from the existing exponents of x and y.
Use the law of exponent known as the power to power rule to justify this step.
( We take out 3 because to be a cube implies that any expression must have an outer exponent,
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